Given an array $$$a$$$ of integers of size $$$n$$$, we say that a position $$$1 \le i \le n$$$ is blocked if $$$a_i$$$ can be expressed as the sum of a subset of $$$a_1, a_2, \ldots, a_{i-1}$$$ (i.e. there exist $$$1 \le j_1 \lt j_2 \lt \ldots \lt j_k \le i-1$$$ such that $$$a_{j_1} + a_{j_2} + \ldots + a_{j_k} = a_i$$$). Reorder $$$a$$$ so that no position is blocked or report that it is impossible.

For example, reordering the array [$$$3, 2, 5$$$] to [$$$2, 3, 5$$$] makes position $$$3$$$ blocked, since we can express $$$5 = 2 + 3$$$, but if we reorder it to [$$$3, 5, 2$$$], no position is blocked.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 400$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 200$$$).

The second line contains $$$n$$$ integers, denoting the array $$$a$$$ ($$$\textbf{1} \le a_i \le 100$$$).

Output

For each test case, print any order of $$$a$$$ such that no position is blocked if it exists, otherwise print $$$-1$$$.

Note

In the third test case, the array [$$$3, 1, 2$$$] has no position blocked:

Position $$$1$$$ is not blocked since $$$3$$$ can't be expressed as the sum of a subset of [].

Position $$$2$$$ is not blocked since $$$1$$$ can't be expressed as the sum of a subset of [$$$3$$$].

Position $$$3$$$ is not blocked since $$$2$$$ can't be expressed as the sum of a subset of [$$$3, 1$$$].

Blocked

Examples